From the Gibbs probability
distribution for a
gas of classical particles interacting through the repulsive and
attractive forces at large temperatures \(T\)  and small enough particle number
density average \(\langle n\rangle \) , one can use the vdW equation
of state (REF )
[see sec.  and Ref. [1]})].
In what follows, to simplify notations,
we will omit angle brackets for statistical averages if it does not
lead to misunderstanding.
Following, e.g., Ref. [2]},
the fluctuations of the particle number \(\omega \)  as the dispersion of the
GCE Gibbs distribution function integrated over the excitation energy
can be expressed in terms of the derivative of particle number-density average.
